Question

There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four numbers is 15, if one of the four numbers is 2, find the other 3 numbers

Answer 1

Let the 4 numbers be a , b , c and d
Mean of the first 2 numbers, a and b = 4
$\text{So},a+b=4\times 2=8—\left(i\right)$
Mean of the first 3 numbers, a, b and c = 9
$\text{So},a+b+c=9\times 3=27–\left(ii\right)$
From equations (i) and (ii),
Third number, c = 27 -8 = 19
Mean of all the 4 numbers = 15
$\text{So},a+b+c+d=15\times 4=60–\left(iii\right)$
From equations (ii) and (iii),
Fourth number,d = 60 - 27 = 33
Now, we got 2 unknown numbers; c = 19 and d = 33
It is given in the question that one of the numbers is 2.
So, let a = 2
Therefore, the third unknown number, b = 60 - (19 +33 +2)
$\Rightarrow b=6$
Hence, the three other numbers are 6, 19 and 33